Question

Consider tossing a coin and rolling a four-sided die (with the numbers 1 through 4 printed on the sides).

(a) Describe the sample space.

(b) Whatistheprobabilityofrollingaheadsandanevennumber?

(c) What are the odds of rolling a heads and an even number?

(d) What is the probability of rolling a heads?

(e) What are the odds against rolling a heads?

Determine whether or not the following statements are correct or incorrect and explain why (Be thorough and clear in your explanation!):

(a) A person says “the odds of rolling a 1 on a standard six-sided die is 1/6.”

(b) In the past five seasons,cross town football riva ls the Quaker sand the Comet shave played

each other with the Comets winning twice and the Quakers winning three times. Someone

says “the odds in favor of the Quakers winning are 3:5.”

(c) If the odds in favor of an event occurring are A to B, then the probability of the event

occurring is A/(A+B).

(d) An event with probability 75% means that the event is three times more likely to occur than

not occur.

Answer 1

Let H shows the head and T shows the tail. When a rdie is rolled possible outcomes are 1, 2, 3, and 4.

Required sample space is

Since all the outcomes are equally likely so probability of each outcome is 1/8.

(b)

The probability of rolling a heads and an even number is

(c)

Out of 8 outcomes, 2 shows head and even number. That is 2 are in favor and 6 are not. So the odds of rolling a heads and an even number are

2 : 6 = 1 : 3

(d)

P(heads) = 4/8 = 1/2 = 0.5

(e)

Odds:

4 : 4 = 1 : 1